binomial theorem

The binomial theorem is a method of expanding the binomial expression
(x + y)n into a finite or infinite series
of powers of x and y, where n is a number either
integral or fractional, positive or negative, rational
or irrational; thus

The binomial theorem was discovered by Isaac Newton
about 1666, and was first published in 1704 in the second appendix to Newton's
Optics. That particular case of the theorem when n is
a positive integer was known to mathematicians prior to Newton (e.g., Briggs
and Pascal), and Newton himself gave no demonstration
of the truth of his theorem.